Introduction to algorithms type of algorithm

Question

I'm learning algorithms and I'm reading the book "introduction to algorithms 3rd edition", and in a problem section it describes the next problem :

Describe a O(n*log(n))-time algorithm that, given a set S of n integers and another integer x, determines whether or not there exist two elements in S whose sum is exactly x.

And I don't know if it propose and ordered Set or an unordered Set?

Answer 1

Let x be the sum you want to have. First sort the array. Then for each element in array (a[i]), find if (xa[i]) exists in the array using binary search.

The pseudo code :

 sort(a,n)
 for i : 1 to n
     if(binary_search(a,i+1,n-1,x-a[i]))
          return true
 return false

Other method: After sorting, use two pointers first and last to check:

 while(first < last) {
        if(a[first]+a[last] == x) return true;
        else if(a[first]+a[last] < x) first++;
       else if(a[first]+a[last] > x) last--;
    }
    return false;

Answer 2

Given a sorted array, you can find if there's a pair that sums to x with with O(n) arithmetic operations.

i := 0
j := len(A) - 1
while i < j {
    if A[i] + A[j] < x {
        i += 1
    } else if A[i] + A[j] == x {
        return true
    } else if A[i] + A[j] > x {
        j -= 1
    }
}
return false

Given this, you can determine if any array contains a pair of elements that sums to x using O(n log n) arithmetic operations by sorting the array, and then using the algorithm above.